Generalised terminants are produced when the coefficients of the two types of series
considered in Ch. 7 are set equal toΓ(pk+q), where pandqare both real and positive and the
variablez is altered to z
β
, where βcan be much greater than unity. Ch. 9 is concerned with the
derivation of the MB-regularised forms for the regularised values of both types of generalised
terminants over the entire complex plane, which are presented in Propositions 4 and 5. These
results are then simplified by considering special cases of p, the first where it is the reciprocal of a
natural natural number and the second, where it equals 2. The chapter concludes by evaluating the
regularised value of a Type II generalised terminant withβ=6,p=1 andq=1/5 using the various
MB-regularised forms that apply over the principal branch forz. Because there is no known special
function equivalent for this asymptotic series, the results from this study serve as a test-bed for the
results in the following chapter. Nevertheless, it is found that the regularised values obtained from
the two MB-regularised forms for each of the six common regions of the overlapping domains of
convergence equal one another for both small and large values of|z|.
